Points, skyrmions and torons in chiral nematic droplets

Flowing Liquid Crystal Torons Around Obstacles

Liquid crystal torons, localized topological structures, are known for their stability and dynamic behaviour in response to external stimuli, making them attractive for advanced material applications. In this study, we investigate the flow of torons in chiral nematic liquid crystals around obstacles. We simulate the fluid flow and director field interactions using a hybrid numerical method combining lattice Boltzmann and finite difference techniques. Our results reveal that the toron dynamical behaviour depends strongly on the impact parameter from the obstacle. At impact parameters smaller than half cholesteric pitch, the flowing toron is destabilized by the interaction with the obstacle; otherwise, the flowing toron follows a trajectory with a deflection which decays exponentially with the impact parameter. Additionally, we explore the scattering of torons by multiple obstacles, providing insights into how the dynamics of these structures respond to complex environments.

Photonic features of blue phase liquid crystals under curved confinement

Blue phase (BP) liquid crystals represent a fascinating state of soft matter that showcases unique optical and electro-optical properties. Existing between chiral nematic and isotropic phases, BPs are characterized by a three-dimensional cubic lattice structure resulting in selective Bragg reflections of light and consequent vivid structural colors. However, the practical realization of these material systems is hampered by their narrow thermal stability and multi-domain crystalline nature. This feature article provides an overview of the efforts devoted to stabilizing these phases and creating monodomain structures. In particular, it delves into the complex relationship between geometrical confinement, induced curvature, and the structural stability and photonic features of BPs. Understanding the interaction of curved confinement and structural stability of BPs proves crucially important for the integration of these materials into flexible and miniaturized devices. By shedding light on these critical aspects, this feature review aims to highlight the significance of understanding the coupling effects of physical and mechanical forces on the structural stability of these systems, which can pave the way for the development of efficient and practical devices based on BP liquid crystals.

Understanding directed assembly of concentrated nanoparticles at energetically heterogeneous interfaces of cholesteric liquid crystal droplets

Colloidal self-assembly has gained significant interest in scientific and technological advances. We investigated the self-assembly of the colloids at fluidic interfaces that mediate elastic interactions. Whereas past studies have reported the assembly of micrometer- or molecular-sized species at aqueous interfaces of liquid crystals (LCs), herein we study the assembly of intermediate-sized nanoparticles. Specifically, surface-modified silica nanoparticles (50 to 500 nm) were adsorbed at the liquid crystal-water interfaces and their positioning was investigated using electron microscopy after polymerization. The study revealed that the electric double layer forces and the elastic forces caused by LC strain are dominant in the assembly of nanoparticles and their contributions can be tuned to direct the self-assembly guided by the sub-interface symmetry of confined cholesteric LCs. At high ionic strengths, we observed a strong localization of nanoparticles at the defects, whereas intermediate strengths resulted in their partial enrichment into cholesteric fingerprint patterns with an interaction energy of ≈3 k_BT. This result is comparable with the calculations based on the strength of the binary interactions of the nanoparticles. The findings also support the role of ion partitioning at the LC-aqueous interfaces on the formation of the assemblies. The results can be utilized for applications in sensors, microelectronics, and photonics.

Neural networks determination of material elastic constants and structures in nematic complex fluids

Supervised machine learning and artificial neural network approaches can allow for the determination of selected material parameters or structures from a measurable signal without knowing the exact mathematical relationship between them. Here, we demonstrate that material nematic elastic constants and the initial structural material configuration can be found using sequential neural networks applied to the transmmited time-dependent light intensity through the nematic liquid crystal (NLC) sample under crossed polarizers. Specifically, we simulate multiple times the relaxation of the NLC from a random (qeunched) initial state to the equilibirum for random values of elastic constants and, simultaneously, the transmittance of the sample for monochromatic polarized light. The obtained time-dependent light transmittances and the corresponding elastic constants form a training data set on which the neural network is trained, which allows for the determination of the elastic constants, as well as the initial state of the director. Finally, we demonstrate that the neural network trained on numerically generated examples can also be used to determine elastic constants from experimentally measured data, finding good agreement between experiments and neural network predictions.

Spontaneous electric-polarization topology in confined ferroelectric nematics

Topological textures have fascinated people in different areas of physics and technologies. However, the observations are limited in magnetic and solid-state ferroelectric systems. Ferroelectric nematic is the first liquid-state ferroelectric that would carry many possibilities of spatially-distributed polarization fields. Contrary to traditional magnetic or crystalline systems, anisotropic liquid crystal interactions can compete with the polarization counterparts, thereby setting a challenge in understating their interplays and the resultant topologies. Here, we discover chiral polarization meron-like structures, which appear during the emergence and growth of quasi-2D ferroelectric nematic domains. The chirality can emerge spontaneously in polar textures and can be additionally biased by introducing chiral dopants. Such micrometre-scale polarization textures are the modified electric variants of the magnetic merons. Both experimental and an extended mean-field modelling reveal that the polarization strength plays a dedicated role in determining polarization topology, providing a guide for exploring diverse polar textures in strongly-polarized liquid crystals.

Continuous generation of topological defects in a passively driven nematic liquid crystal

Synthetic active matter is emerging as the prime route for the realisation of biological mechanisms such as locomotion, active mixing, and self-organisation in soft materials. In particular, passive nematic complex fluids are known to form out-of-equilibrium states with topological defects, but their locomotion, activation and experimental realization has been developed and understood to only a limited extent. Here, we report that the concentration-driven flow of small molecules triggers turbulent flow in the thin film of a nematic liquid crystal that continuously generates pairs of topological defects with an integer topological charge. The diffusion results in the formation of counter-rotating vortex rolls in the liquid crystal, which above a velocity threshold transform into a turbulent flow with continuous generation and annihilation of the defect pairs. The pairs of defects are created by the self-amplifying splay instability between the vortices, until a pair of oppositely charged defects is formed.

It has been known that spontaneous defect formation and annihilation can be triggered by turbulent flows in active nematic liquid crystals. Here, Mur et al. show a complementary mechanism induced by the flow of foreign organic molecules into the liquid crystal following the concentration gradient.

Elastic Instability of Cubic Blue Phase Nano Crystals in Curved Shells

Many crystallization processes, including biomineralization and ice-freezing, occur in small and curved volumes, where surface curvature can strain the crystal, leading to unusual configurations and defect formation. The role of curvature on crystallization, however, remains poorly understood. Here, we study the crystallization of blue phase (BP) liquid crystals under curved confinement, which provides insights into the mechanism by which BPs reconfigure their three-dimensional lattice structure to adapt to curvature. BPs are a three-dimensional assembly of high-chirality liquid crystal molecules arranged into body-centered (BPI) or simple cubic (BPII) symmetries. BPs with submicrometer cubic-crystalline lattices exhibit tunable Bragg reflection and submillisecond response time to external stimuli such as an electric field, making them attractive for advanced photonic materials. In this work, we have systematically studied BPs confined in spherical shells with well-defined curvature and boundary conditions. The optical behavior of shells has also been examined at room temperature, where the cholesteric structure forms. In the cholesteric phase, perpendicular anchoring generates focal conic domains on the shell's surface, which transition into stripe patterns as the degree of curvature increases. Our results demonstrate that both higher degrees of curvature and strong spatial confinement destabilize BPI and reconfigure that phase to adopt the structure and optical features of BPII. We also show that the coupling of curvature and confinement nucleates skyrmions at greater thicknesses than those observed for a flat geometry. These findings are particularly important for integrating BPs into miniaturized and curved/flexible devices, including flexible displays, wearable sensors, and smart fabrics.

Nematic bits and universal logic gates

Liquid crystals (LCs) can host robust topological defect structures that essentially determine their optical and elastic properties. Although recent experimental progress enables precise control over nematic LC defects, their practical potential for information storage and processing has yet to be explored. Here, we introduce the concept of nematic bits (nbits) by exploiting a quaternionic mapping from LC defects to the Poincaré-Bloch sphere. Through theory and simulations, we demonstrate how single-nbit operations can be implemented using electric fields, to construct LC analogs of Pauli, Hadamard, and other elementary logic gates. Using nematoelastic interactions, we show how four-nbit configurations can realize universal classical NOR and NAND gates. Last, we demonstrate the implementation of generalized logical functions that take values on the Poincaré-Bloch sphere. These results open a route toward the implementation of classical digital and nonclassical continuous computation strategies in topological soft matter systems.

Chiral Liquid Crystal Microdroplets for Sensing Phospholipid Amphiphiles

Designing simple, sensitive, fast, and inexpensive readout devices to detect biological molecules and biomarkers is crucial for early diagnosis and treatments. Here, we have studied the interaction of the chiral liquid crystal (CLC) and biomolecules at the liquid crystal (LC)-droplet interface. CLC droplets with high and low chirality were prepared using a microfluidic device. We explored the reconfiguration of the CLC molecules confined in droplets in the presence of 1,2-diauroyl-sn-glycero3-phosphatidylcholine (DLPC) phospholipid. Cross-polarized optical microscopy and spectrometry techniques were employed to monitor the effect of droplet size and DLPC concentration on the structural reorganization of the CLC molecules. Our results showed that in the presence of DLPC, the chiral LC droplets transition from planar to homeotropic ordering through a multistage molecular reorientation. However, this reconfiguration process in the low-chirality droplets happened three times faster than in high-chirality ones. Applying spectrometry and image analysis, we found that the change in the chiral droplets' Bragg reflection can be correlated with the CLC-DLPC interactions.

Numerical modeling of optical modes in topological soft matter

Vector and vortex laser beams are desired in many applications and are usually created by manipulating the laser output or by inserting optical components in the laser cavity. Distinctly, inserting liquid crystals into the laser cavity allows for extensive control over the emitted light due to their high susceptibility to external fields and birefringent nature. In this work we demonstrate diverse optical modes for lasing as enabled and stablised by topological birefringent soft matter structures using numerical modelling. We show diverse structuring of light-with different 3D intensity and polarization profiles-as realised by topological soft matter structures in radial nematic droplet, in 2D nematic cavities of different geometry and including topological defects with different charges and winding numbers, in arbitrary varying birefringence fields with topological defects and in pixelated birefringent profiles. We use custom written FDFD code to calculate emergent electromagnetic eigenmodes. Control over lasing is of a particular interest aiming towards the creation of general intensity, polarization and topologically shaped laser beams.

Structural properties and ring defect formation in discotic liquid crystal nanodroplets

In this work, we performedNpTMonte Carlo simulations of a Gay-Berne discotic liquid crystal confined in a spherical droplet under face-on anchoring and fixed pressure. We find that, in contrast to the unbounded system, a plot of the order parameter as function of temperature does not show a clear evidence of a first-order isotropic-nematic transition. We also find that the impossibility of simultaneously satisfy the uniform director field requirement of a nematic phase with the radial boundary conditions, results in the appearance of a ring disclination line as a stress release mechanism in the interior of the droplet. Under further cooling, a columnar phase appears at the center of the droplet.

Polymer-Dispersed Cholesteric Liquid Crystal under Homeotropic Anchoring: Electrically Induced Structures with λ1/2-Disclination

Orientational structures of polymer-dispersed cholesteric liquid crystal under homeotropic anchoring and their transformations under the action of an electric field are studied. The switching of cholesteric droplets between different topological states are experimentally and theoretically demonstrated. Structures with λ+1/2-disclination are found and considered. These structures are formed during the transformation of a twisted toroidal configuration induced by a decrease in the electric field when a relative chiral parameter N0>6.3. The transformation of the initial structure with a bipolar distribution of the helix axis into a twisted toroidal configuration and then into a structure with λ+1/2-disclination is investigated in detail. The behavior of these structures under the influence of an external electric field, as well as the appearance of structures with λ−1/2-disclination, are studied. Obtained results are promising for the development of optical materials with programmable properties.

Oblique light incidence method to study topological defects in nematic layers with conical boundary conditions

A polarization microscopy method to investigate the orientational structures and boojums formed in the chiral and achiral nematic layers under conical (tilted) boundary conditions has been developed. Oblique light incidence on nematic layer is used, due to which the phase difference between the ordinary and extraordinary waves depends on the director's azimuthal angle. The phase difference gets maximal when the director azimuthal angle of achiral nematic [Formula: see text] and an azimuthal angle at the center of the chiral nematic layer [Formula: see text] independently of the total twist angle [Formula: see text]. It has been found that the [Formula: see text] boojums with the phase [Formula: see text] and [Formula: see text] are formed in achiral and chiral nematics, respectively, at the director tilt angle [Formula: see text] at the interface. In addition, the defectless structure of chiral nematic with the periodically variable azimuthal director angle on the substrates has been studied.

Interactions of charged microrods in chiral nematic liquid crystals

We study the pair interaction of charged silica microrods in chiral nematic liquid crystals and show that the microrods with homeotropic surface anchoring form a bound state due to the competing effect of electrostatic (Coulomb) and elastic interactions. The robustness of the bound state is demonstrated by applying external electrical and mechanical forces that perturbs their equilibrium position as well as orientation. In the bound state we have measured the correlated thermal fluctuations of the position, using two-particle cross-correlation spectroscopy that uncovers their hydrodynamic interaction. These findings reveal unexplored aspects of liquid-crystal dispersions which are important for understanding the assembly and dynamics of nano- and microparticles in chiral nematic liquid crystals.

Layering transitions and metastable structures of cholesteric liquid crystals in cylindrical confinement

Our study of cholesteric lyotropic chromonic liquid crystals in cylindrical confinement reveals the topological aspects of cholesteric liquid crystals. The double-twist configurations we observe exhibit discontinuous layering transitions, domain formation, metastability, and chiral point defects as the concentration of chiral dopant is varied. We demonstrate that these distinct layer states can be distinguished by chiral topological invariants. We show that changes in the layer structure give rise to a chiral soliton similar to a toron, comprising a metastable pair of chiral point defects. Through the applicability of the invariants we describe to general systems, our work has broad relevance to the study of chiral materials.

Photo-reconfigurable twisting structure in chiral liquid crystals triggered by photoresponsive surface

Shape-transformable molecular additives with photoresponsivity, such as azobenzene or spiropyran, in matter are known to decrease the local order parameter and lead to drastic state variations under light irradiation. For example, a liquid crystalline state can be transformed to an isotropic liquid state by photo-exciting a tiny amount of azobenzene additives from trans- to cis-conformers. On the other hand, structural or shape transformation without changing the phase state is also intriguing since it offers an opportunity for manipulating specific structures. Here, we demonstrate an active control of the topology of chiral particle-like twisting structures, dubbed toron, by light. Interestingly, the individual twisting structure is fully reconfigurable between spherical and unique branched topological states. We reveal that the shape transformation is driven by the free-energy competition between the variation of surface anchoring strength and the elastic energy stored in the twisting structure. The mean-field simulation based on the Landau-de Gennes framework shows that the elastic anisotropy plays the dominant role in modifying the toron topology upon weak anchoring. The results offer a new path for understanding the process of topology-involved shape transformation and fabrication of novel functional materials.

Design of nematic liquid crystals to control microscale dynamics

The dynamics of small particles, both living such as swimming bacteria and inanimate, such as colloidal spheres, has fascinated scientists for centuries. If one could learn how to control and streamline their chaotic motion, that would open technological opportunities in the transformation of stored or environmental energy into systematic motion, with applications in micro-robotics, transport of matter, guided morphogenesis. This review presents an approach to command microscale dynamics by replacing an isotropic medium with a liquid crystal. Orientational order and associated properties, such as elasticity, surface anchoring, and bulk anisotropy, enable new dynamic effects, ranging from the appearance and propagation of particle-like solitary waves to self-locomotion of an active droplet. By using photoalignment, the liquid crystal can be patterned into predesigned structures. In the presence of the electric field, these patterns enable the transport of solid and fluid particles through nonlinear electrokinetics rooted in anisotropy of conductivity and permittivity. Director patterns command the dynamics of swimming bacteria, guiding their trajectories, polarity of swimming, and distribution in space. This guidance is of a higher level of complexity than a simple following of the director by rod-like microorganisms. Namely, the director gradients mediate hydrodynamic interactions of bacteria to produce an active force and collective polar modes of swimming. The patterned director could also be engraved in a liquid crystal elastomer. When an elastomer coating is activated by heat or light, these patterns produce a deterministic surface topography. The director gradients define an activation force that shapes the elastomer in a manner similar to the active stresses triggering flows in active nematics. The patterned elastomer substrates could be used to define the orientation of cells in living tissues. The liquid-crystal guidance holds a major promise in achieving the goal of commanding microscale active flows.

Polymer Dispersed Cholesteric Liquid Crystals With a Toroidal Director Configuration under an Electric Field

The electro-optical properties of polymer dispersed liquid crystal (PDLC) films are highly dependent on the features of the contained liquid crystal (LC) droplets. Cholesteric LC droplets with homeotropic boundaries can form several topologically different orientational structures, including ones with single and more point defects, layer-like, and axisymmetric twisted toroidal structures. These structures are very sensitive to an applied electric field. In this work, we have demonstrated experimentally and by computer simulations that twisted toroidal droplets reveal strong structural response to the electric field. In turn, this leads to vivid changes in the optical texture in crossed polarizers. The response of droplets of different sizes were found to be equivalent in terms of dimensionless parameters. In addition, the explanation of this phenomenon showed a comparison of theoretical and experimental structural response curves aids to determine the shape of the droplet. Finally, we demonstrated that the addition of a dichroic dye allows such films to be used as optical filters with adjustable color even without polarizers.

Polarized epifluorescence microscopy and the imaging of nematic liquid crystals in highly curved geometries

We develop polarized epifluorescence microscopy (PFM), a technique to qualitatively determine a director field, even when refraction effects are too strong to use optical polarized microscopy. We present the basic theory behind the technique and cover in detail the experimental setup. We validate PFM on the well-studied cases of a planar nematic cell, spherical nematic droplets, and a cylindrical capillary filled with nematic liquid crystal. Last, we use nematic capillary bridges to demonstrate that PFM can indeed provide measurements of the director field, even when refraction effects are large.

Swelling Cholesteric Liquid Crystal Shells to Direct the Assembly of Particles at the Interface

Cholesteric liquid crystals can exhibit spatial patterns in molecular alignment at interfaces that can be exploited for particle assembly. These patterns emerge from the competition between bulk and surface energies, tunable with the system geometry. In this work, we use the osmotic swelling of cholesteric double emulsions to assemble colloidal particles through a pathway-dependent process. Particles can be repositioned from a surface-mediated to an elasticity-mediated state through dynamically thinning the cholesteric shell at a rate comparable to that of colloidal adsorption. By tuning the balance between surface and bulk energies with the system geometry, colloidal assemblies on the cholesteric interface can be molded by the underlying elastic field to form linear aggregates. The transition of adsorbed particles from surface regions with homeotropic anchoring to defect regions is accompanied by a reduction in particle mobility. The arrested assemblies subsequently map out and stabilize topological defects. These results demonstrate the kinetic arrest of interfacial particles within definable patterns by regulating the energetic frustration within cholesterics. This work highlights the importance of kinetic pathways for particle assembly in liquid crystals, of relevance to optical and energy applications.

Optical Textures and Orientational Structures in Cholesteric Droplets with Conical Boundary Conditions

Cholesteric droplets dispersed in polymer with conical boundary conditions have been studied. The director configurations are identified by the polarising microscopy technique. The axisymmetric twisted axial-bipolar configuration with the surface circular defect at the droplet’s equator is formed at the relative chirality parameter N0≤2.9. The intermediate director configuration with the deformed circular defect is realised at 2.9<N0<3.95, and the layer-like structure with the twisted surface defect loop is observed at N0≥3.95. The cholesteric layers in the layer-like structure are slightly distorted although the cholesteric helix is untwisted.

Self-assembled toron-like structures in inverse nematic gels

A novel form of nematic gel (N-gel) wherein bright flower-like domains (BFDs) rich in gelator fibres are embedded in a matrix of liquid crystal (LC) molecules has been reported. These gels which we denote as inverse N-gels are unlike typical N-gels in which the LC is encapsulated within an aggregated network of gelator molecules. The self-organization of the helical gelator fibres within the BFDs leads to the creation of localized toron-like structures that are topologically protected due to their skyrmion director profile. Optical and confocal microscopy have been used to deduce the LC director configuration, in order to understand possible intermolecular interactions that can lead to the formation of the twisted structures and the inverse N-gels.

Topological solitons, cholesteric fingers and singular defect lines in Janus liquid crystal shells

Topological solitons are non-singular but topologically nontrivial structures in fields, which have fundamental significance across various areas of physics, similar to singular defects. Production and observation of singular and solitonic topological structures remain a complex undertaking in most branches of science - but in soft matter physics, they can be realized within the director field of a liquid crystal. Additionally, it has been shown that confining liquid crystals to spherical shells using microfluidics resulted in a versatile experimental platform for the dynamical study of topological transformations between director configurations. In this work, we demonstrate the triggered formation of topological solitons, cholesteric fingers, singular defect lines and related structures in liquid crystal shells. We show that to accommodate these objects, shells must possess a Janus nature, featuring both twisted and untwisted domains. We report the formation of linear and axisymmetric objects, which we identify as cholesteric fingers and skyrmions or elementary torons, respectively. We then take advantage of the sensitivity of shells to numerous external stimuli to induce dynamical transitions between various types of structures, allowing for a richer phenomenology than traditional liquid crystal cells with solid flat walls. Using gradually more refined experimental techniques, we induce the targeted transformation of cholesteric twist walls and fingers into skyrmions and elementary torons. We capture the different stages of these director transformations using numerical simulations. Finally, we uncover an experimental mechanism to nucleate arrays of axisymmetric structures on shells, thereby creating a system of potential interest for tackling crystallography studies on curved spaces.

Thermo-Optical Generation of Particle-Like Structures in Frustrated Chiral Nematic Film

The creation of metastable particle-like structures in frustrated (unwound) chiral nematic film containing light-absorbing additive is studied. It is shown that such localized structures can be generated by the thermo-optical action of a focused laser beam or arise spontaneously at a phase transition from an isotropic to a liquid crystal state. Observed axisymmetric patterns resemble cholesteric spherulites with toroidal double-twisted director-field configuration.

Orientational structures in cholesteric droplets with homeotropic surface anchoring

The dependency of orientational structures in cholesteric droplets with homeotropic surface anchoring on the helicity parameter has been studied by experiment and simulations. We have observed a sequence of structures, in which the director configurations and topological defects were identified by comparison of polarized microscopy pictures with simulated textures. A toron-like and low-symmetry intermediate layer-like structures have been revealed and studied in detail. The ranges of stability of the observed structures have been summarized in a general diagram and explained by the helicity parameter dependence of the free energy terms.

Ray-based optical visualisation of complex birefringent structures including energy transport

We propose an efficient method to simulate light propagation in lossless and non-scattering uniaxial birefringent media, based on a standard ray-tracing technique supplemented by a newly-derived transport equation for the electric field amplitude along a ray and a tailored interpolation algorithm for the reconstruction of the electromagnetic fields. We show that this algorithm is accurate in comparison to a full solution of Maxwell's equations when the permittivity tensor of the birefringent medium typically varies over a length much bigger than the wavelength. We demonstrate the usefulness of our code for soft matter by comparing experimental images of liquid crystal droplets with simulated bright-field optical micrographs, and conclude that our method is more general than the usual Jones method, which is only valid under polarised illumination conditions. We also point out other possible applications of our method, including liquid crystal based flat element design and diffraction pattern calculations for periodic liquid crystal samples.

Hydrodynamic rotlet dipole driven by spinning chiral liquid crystal droplets

Chirality is an essential evolutionary-conserved physical aspect of swimming microorganisms. However, the role of chirality on the hydrodynamics of such microswimmers is still being elucidated. Hydrodynamic theories have so far predicted that, under a torque-free condition satisfied in the system of microswimmers, a rotlet dipole generating a twisting flow is the leading-order singularity of the chiral flow field. Nevertheless, such a chiral flow field has never been experimentally detected. Here we explore a hydrodynamic field generated in a system of a chiral microswimmer, where a droplet of a cholesteric liquid crystal (CLC) exhibits helical and spinning motions in surfactant solutions due to a chiral nonequilibrium cross coupling between the rotation and the Marangoni flow. Combining measurement of the flow field around the spinning CLC droplets and a computational flow modeling, we revealed that the CLC droplets generate a flow field of a rotlet dipole. Remarkably, we found that the chiral component of the flow field decays with distance r as r^{-3}, which is consistent with the theoretical prediction for the flow field produced by a point singularity of a rotlet dipole. Our findings will promote the understanding of roles of chirality on the hydrodynamics in active matter as well as liquid crystals.

Spherical-cap droplets of a photo-responsive bent liquid crystal dimer

Using a photo-responsive dimer exhibiting the transition between nematic (N) and twist-bend nematic (NTB) phases, we prepared spherical cap-shaped droplets on solid substrates exposed to air. The internal director structures of these droplets vary depending on the phase and on the imposed boundary conditions. The structural switching between the N and NTB phases was successfully performed either by temperature control or by UV light-irradiation. The N phase is characterized by an extremely small bend elastic constant K3, and surprisingly, we found that the droplet-air interface induces a planar alignment, in contrast to that seen for typical calamitic liquid crystals. As a consequence, the director configuration was stabilized in a structure substantially different from that normally found in conventional nematic liquid crystalline droplets. In the twist-bend nematic droplets characteristic structures with macroscopic length scales were formed, and they were well controlled by the droplet size. These results indicated that a continuum theory is effective in describing the stabilization mechanism of the macroscopic structure even in the twist-bend nematic liquid crystal droplets exhibiting director modulations on a scale of several molecular lengths.

Curvature-Induced Twist in Homeotropic Nematic Tori

We confine a nematic liquid crystal with homeotropic anchoring to stable toroidal droplets and study how geometry affects the equilibrium director configuration. In contrast to the case of cylindrical confinement, we find that the equilibrium state is chiral-a twisted and escaped radial director configuration. Furthermore, we find that the magnitude of the twist distortion increases as the ratio of the ring radius to the tube radius decreases; we confirm this with computer simulations of optically polarized microscopy textures. In addition, numerical calculations also indicate that the local geometry indeed affects the magnitude of the twist distortion. We further confirm this curvature-induced twisting using bent cylindrical capillaries.

Nematic colloidal knots in topological environments

The role of environment in shaping material properties is of great significance, but less is known about how non-trivial topology of the environment couples to material states, which can be of non-trivial topology themselves. In this paper, we demonstrate the role of the topology of the environment on the formation of complex nematic fields and defect structures, specifically in the system of nematic colloidal knots. The topological environments around knotted colloidal particles are suggested to exist as spherical surface-patterned nematic cavities imposing radial, uniform or hyperbolic nematic profiles. We show that topologically different nematic environments significantly affect and create differences in the colloidal field structure created within the environment, such as the location, profile and number of topological defects. Specifically, we demonstrate that topological environments in combination with knotted colloidal particles of non-trivial topology lead to the formation of diverse nematic knotted and linked fields. These fields are different adaptations of the knotted shape of the colloidal particles, creating knots and links of topological defects as well as escaped-core defect-like solitonic structures. These are observed in chiral nematic media but here are stabilised in achiral nematic media as a result of the distinct shape of the knotted colloidal particle, with a double helix segment and nematic environmental patterns. More generally, this paper is a contribution towards understanding the role of environment, especially its topology, on the response and defect formation in elastic fields, such as in nematic liquid crystal colloids.

Topology-dependent self-structure mediation and efficient energy conversion in heat-flux-driven rotors of cholesteric droplets

When heat flux is applied to a chiral liquid crystal, unidirectional rotation is induced around the flux axis, as first discovered by Otto Lehmann in 1900. In recent years, this heat-flux-induced phenomenon has been studied mostly in droplets of cholesteric liquid crystals undergoing phase transition from the isotropic to cholesteric phase, i.e., in the coexistence region, which occurs over a very narrow temperature range. Here, we report that the heat-flux-induced rotation can be stabilised by the use of a dispersion system, in which the cholesteric droplets are dispersed in a viscous and poorly miscible isotropic solvent. Interestingly, the phenomenon is found to be topology dependent. Moreover, the rotation is not only stable but also more efficient than that in the known systems. We describe in detail how the dynamics of the heat-flux-induced rotation are altered in the present dispersion system.

The Lehmann effect describes the spontaneous rotation of cholesteric liquid crystals in response to heat input. Here, the authors stabilise it by dispersing cholesteric droplets into a poorly miscible solvent and show dependences of rotation speed and conversion efficiency on the topological states.

Nematic Liquid-Crystal Colloids

This article provides a concise review of a new state of colloidal matter called nematic liquid-crystal colloids. These colloids are obtained by dispersing microparticles of different shapes in a nematic liquid crystal that acts as a solvent for the dispersed particles. The microparticles induce a local deformation of the liquid crystal, which then generates topological defects and long-range forces between the neighboring particles. The colloidal forces in nematic colloids are much stronger than the forces in ordinary colloids in isotropic solvents, exceeding thousands of kBT per micrometer-sized particle. Of special interest are the topological defects in nematic colloids, which appear in many fascinating forms, such as singular points, closed loops, multitudes of interlinked and knotted loops or soliton-like structures. The richness of the topological phenomena and the possibility to design and control topological defects with laser tweezers make colloids in nematic liquid crystals an excellent playground for testing the basic theorems of topology.

Topology-commanded optical properties of bistable electric-field-induced torons in cholesteric bubble domains

Nowadays, complicated topological defects enable many experimental manipulations and configurational simulations of active soft matter for optical and photonic applications. Investigation of topological defects in soft anisotropic materials enables one to better understand three-dimensional orientation fields in cholesteric liquid crystals. Here, we describe optical properties of bistable bubble domain (BD) texture torons in a thin layer of cholesteric liquid crystal (CLC), frustrated by homeotropic anchoring conditions, and reliably switchable by a random process. The control of macroscopic optical density and diffraction efficiency of the BD texture is demonstrated by a selection of a confinement ratio of the CLC. Experimentally reconstructed CLC director profile reveals the topology of BD torons allowing consideration of naturally occurring BD texture for applications in optical and photonic devices, which are bistably switchable between active and transparent optical states.

Wide area mapping of liquid crystal devices with passive and active command layers

We track the non-uniformity of a wide area liquid crystal device using multiple cross-polarized intensity measurements. They give us not only accurate estimates of the core physical liquid crystal parameters, such as elastic constants, but also spatial maps of the device properties, including the liquid crystal thickness and pretilt angle. A bootstrapping statistical analysis, coupled with the multiple measurements, gives us reliable error bars on all the measured parameters.

Bipolar configuration with twisted loop defect in chiral nematic droplets under homeotropic surface anchoring

Optical textures and appropriate orientational structures have been studied within droplets of chiral nematic dispersed in polymer assigning the homeotropic anchoring. The helix axis of the chiral structure inside droplets forms the bipolar configuration. The optical droplet textures were analysed in the unpolarised light, analyser switching-off scheme and in crossed polarisers. The twisted loop defect reveals itself convincingly in all schemes. Its appearance at the optical patterns of the chiral nematic droplets has been examined depending on their size and the aspect direction. The existence of the defect has been verified by the structural and optical calculations. The effect of an electric field on both the defect line shape and the orientational structure of chiral nematic has been studied.

Biomaterial microlasers implantable in the cornea, skin, and blood

Stand-alone laser particles that are implantable into biological tissues have potential to enable novel optical imaging, diagnosis and therapy. Here we demonstrate several types of biocompatible microlasers and their lasing action within biological systems. Dye-doped polystyrene beads were embedded in the cornea and optically pumped to generate narrowband emission. We fabricated microbeads with poly(lactic-co-glycolic acid) and poly(lactic acid)-substances approved for medical use-and demonstrate lasing from within tissues and whole blood. Furthermore, we demonstrate biocompatible cholesterol-derivative microdroplet lasers via self-assembly to an onion-like radially-resonant photonic crystal structure.

Role of anchoring energy on the texture of cholesteric droplets: Finite-element simulations and experiments

We present a numerical method to compute defect-free textures inside cholesteric domains of arbitrary shape. This method has two interesting properties, namely a robust and fast quadratic convergence to a local minimum of the Frank free energy, thanks to a trust region strategy. We apply this algorithm to study the texture of cholesteric droplets in coexistence with their isotropic liquid in two cases: when the anchoring is planar and when it is tilted. In the first case, we show how to determine the anchoring energy at the cholesteric-isotropic interface from a study of the optical properties of droplets of different sizes oriented with an electric field. This method is applied to the case of the liquid crystal CCN-37. In the second case, we come back to the issue of the textural transition as a function of the droplet radius between the double-twist droplets and the banded droplets, observed for instance in cyanobiphenyl liquid crystals. We show that, even if this transition is dominated by the saddle-splay Gauss constant K_{4}, as was recently recognized by Yoshioka et al. [Soft Matter 12, 2400 (2016)1744-683X10.1039/C5SM02838H], the anchoring energy does also play an important role that cannot be neglected.

Hidden topological constellations and polyvalent charges in chiral nematic droplets

Topology has an increasingly important role in the physics of condensed matter, quantum systems, material science, photonics and biology, with spectacular realizations of topological concepts in liquid crystals. Here we report on long-lived hidden topological states in thermally quenched, chiral nematic droplets, formed from string-like, triangular and polyhedral constellations of monovalent and polyvalent singular point defects. These topological defects are regularly packed into a spherical liquid volume and stabilized by the elastic energy barrier due to the helical structure and confinement of the liquid crystal in the micro-sphere. We observe, for the first time, topological three-dimensional point defects of the quantized hedgehog charge q=−2, −3. These higher-charge defects act as ideal polyvalent artificial atoms, binding the defects into polyhedral constellations representing topological molecules.

Once a purely mathematical discipline, topology has become an essential tool to investigate physical phenomena such as topological states in liquid crystals. Posnjak et al. observe the existence of 3D point defects of higher than unit topological charge in thermally quenched chiral nematic droplets.

Topological defects in cholesteric liquid crystal shells

We investigate experimentally and numerically the defect configurations emerging when a cholesteric liquid crystal is confined to a spherical shell. We uncover a rich scenario of defect configurations, some of them non-existent in nematic shells, where new types of defects are stabilized by the helical ordering of the liquid crystal. In contrast to nematic shells, here defects are not simple singular points or lines, but have a large structured core. Specifically, we observe five different types of cholesteric shells. We study the statistical distribution of the different types of shells as a function of the two relevant geometrical dimensionless parameters of the system. By playing with these parameters, we are able to induce transitions between different types of shells. These transitions involve interesting topological transformations in which the defects recombine to form new structures. Surprisingly, the defects do not approach each other by taking the shorter distance route (geodesic), but by following intricate paths.

Lasing properties of polymerized chiral nematic Bragg onion microlasers

Dye doped photocurable cholesteric liquid crystal was used to produce solid Bragg onion omnidirectional lasers. The lasers were produced by dispersing and polymerizing chiral nematic LC with parallel surface anchoring of LC molecules at the interface, extracted and transferred into another medium. Lasing characteristics were studied in carrier medium with different refractive index. The lasing in spherical cholesteric liquid crystal was attributed to two mechanisms, photonic bandedge lasing and lasing of whispering-gallery modes. The latter can be suppressed by using a higher index carrier fluid to prevent total internal reflection on the interface of the spheres. Pulse-to-pulse stability and threshold characteristics were also studied and compared to non-polymerized lasers. The polymerization process greatly increases the lasing stability.